How do you determine the number of possible triangles and find the measure of the three angles given $P Q = 12, P R = 15, m ∠ R = 100$ $PQ=12, PR=15, mangleR=100$ ?

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How do you determine the number of possible triangles and find the measure of the three angles given $P Q = 12, P R = 15, m ∠ R = 100$ $PQ=12, PR=15, mangleR=100$ ?

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Answer 1 · 2018-02-26T06:35:07

No solution is possible with the given SSA measurements.

Explanation:

$r = 12, ˆ R = 100, q = 15$ $r = 12, hatR = 100, q = 15$

Since one angle is obtuse, only one solution is possible with the measurements given.

$sin Q = \frac{sin R \cdot q}{r} = \frac{sin 100 \cdot 15}{12}$ $sin Q = (sin R * q) / r = (sin 100 * 15) / 12$

However, side q is greater than r. Therefore $ˆ Q$ $hat Q$ must be greater than $ˆ R$ $hat R$ . As $ˆ R$ $hatR$ is already obtuse, no two obtuse angles exist in a triangle. Hence, no solution is possible with the given SSA measurements.

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How do you determine the number of possible triangles and find the measure of the three angles given $P Q = 12, P R = 15, m ∠ R = 100$ $PQ=12, PR=15, mangleR=100$ ?

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Explanation:

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Science

Math

Humanities

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How do you determine the number of possible triangles and find the measure of the three angles given PQ=12,PR=15,m∠R=100PQ=12, PR=15, mangleR=100?

1 Answer

Explanation:

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How do you determine the number of possible triangles and find the measure of the three angles given $P Q = 12, P R = 15, m ∠ R = 100$ $PQ=12, PR=15, mangleR=100$ ?